As can be seen, for the case \(c_{0} = 1\) , the behavior of the metric near the origin corresponds to an Anti-de Sitter space-time and the Kretschmann scalar has a finite value (\(K=3/200\alpha ^2\) ) (with a nonzero mass). Regular solutions with an Anti-de Sitter core have been studied with a nonlinear electromagnetic source in [1]}. But, for the case \(c_{0} = -2/9\) , the Kretschmann scalar does not become zero and there is a singularity.
In Figure REF , we have shown the full solutions of the field equations from center to infinity by starting from the near origin metric (REF ) and asymptotic solution (17), for \(c_0=1\)  (a solution without horizonThis solution is not a naked solution because the Kretschmann scalar does not diverge.) and for \(c_0=-2/9\)  (black hole case).
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